Escaping abstraction

Jacques Barzun, “History as Counter-Method and Anti-Abstraction,” quoted in Arthur Krystal’s 2007 profile in The New Yorker:

History, like a vast river, propels logs, vegetation, rafts, and debris; it is full of live and dead things, some destined for resurrection; it mingles many waters and holds in solution invisible substances stolen from distant soils. Anything may become part of it; that is why it can be an image of the continuity of mankind. And it is also why some of its freight turns up again in the social sciences: they were constructed out of the contents of history in the same way as houses in medieval Rome were made out of stones taken from the Coliseum. But the special sciences based on sorted facts cannot be mistaken for rivers flowing in time and full of persons and events. They are systems fashioned with concepts, numbers, and abstract relations. For history, the reward of eluding method is to escape abstraction.

Freed from these irrelevancies

Arthur Eddington, The Internal Constitution of the Stars, 1926:

I conceive that the chief aim of the physicist in discussing a theoretical problem is to obtain ‘insight’—to see which of the numerous factors are particularly concerned in any effect and how they work together to give it. For this purpose a legitimate approximation is not just an unavoidable evil; it is a discernment that certain factors—certain complications of the problem—do not contribute appreciably to the result. We satisfy ourselves that they may be left aside; and the mechanism stands out more clearly freed from these irrelevancies. This discernment is only a continuation of a task begun by the physicist before the mathematical premises of the problem could even be stated; for in any natural problem the actual conditions are of extreme complexity and the first step is to select those which have an essential influence on the result—in short, to get hold of the right end of the stick.

Lawrence Krauss, Fear of Physics, 1993:

A physicist, an engineer, and a psychologist are called in as consultants to a dairy farm whose production has been below par. Each is given time to inspect the details of the operation before making a report.

The first to be called is the engineer, who states: “The size of the stalls for the cattle should be decreased. Efficiency could be improved if the cows were more closely packed, with a net allotment of 275 cubic feet per cow. Also, the diameter of the milking tubes should be increased by 4 percent to allow for a greater average flow rate during the milking periods.”

The next to report is the psychologist, who proposes: “The inside of the barn should be painted green. This is a more mellow color than brown and should help induce greater milk flow. Also, more trees should be planted in the fields to add diversity to the scenery for the cattle during grazing, to reduce boredom.”

Finally, the physicist is called upon. He asks for a blackboard and then draws a circle. He begins: “Assume the cow is a sphere. . . .”

This old joke, if not very funny, does illustrate how—at least metaphorically—physicists picture the world. The set of tools physicists have to describe nature is limited. Most of the modern theories you read about began life as simple models by physicists who didn’t know how else to start to solve a problem. These simple little models are usually based on even simpler little models, and so on, because the class of things that we do know how to solve exactly can be counted on the fingers of one, maybe two, hands. For the most part, physicists follow the same guidelines that have helped keep Hollywood movie producers rich: If it works, exploit it. If it still works, copy it.

I like the cow joke because it provides an allegory for thinking simply about the world, and it allows me to jump right in to an idea that doesn’t get written about too much, but that is essential for the everyday workings of science: Before doing anything else, abstract out all irrelevant details!

There are two operative words here: abstract and irrelevant. (Getting rid of irrelevant details is the first step in building any model of the world, and we do it subconsciously from the moment we are born). Doing it consciously is another matter. Overcoming the natural desire not to throw out unnecessary information is probably the hardest and most important part of learning physics. In addition, what may be irrelevant in a given situation is not universal but depends in most cases on what interests you. This leads us to the second operative word: abstraction. Of all the abstract thinking required in physics, probably the most challenging lies in choosing how to approach a problem. The mere description of movement along a straight line—the first major development in modern physics—required enough abstraction that it largely eluded some pretty impressive intellects until Galileo.